Find the Holes in the Graph f(x)=((x-1)(x+3))/((x+1)(x-1))

$f (x) = \frac{(x - 1) (x + 3)}{(x + 1) (x - 1)}$

Step 1

Cancel the common factor of $x - 1$ .

Cancel the common factor.

$f (x) = \frac{(x - 1) (x + 3)}{(x + 1) (x - 1)}$

Rewrite the expression.

$f (x) = \frac{x + 3}{x + 1}$

Step 2

To find the holes in the graph, look at the denominator factors that were cancelled.

$x - 1$

Step 3

To find the coordinates of the holes, set each factor that was cancelled equal to $0$ , solve, and substitute back in to $\frac{x + 3}{x + 1}$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Substitute $1$ for $x$ in $\frac{x + 3}{x + 1}$ and simplify.

Substitute $1$ for $x$ to find the $y$ coordinate of the hole.

$\frac{1 + 3}{1 + 1}$

Simplify.

Add $1$ and $3$ .

$\frac{4}{1 + 1}$

Add $1$ and $1$ .

$\frac{4}{2}$

Divide $4$ by $2$ .

$2$

The holes in the graph are the points where any of the cancelled factors are equal to $0$ .

$(1, 2)$

Step 4